Well, if you have karaoke disks, the best way to try a new song is to look at the ones you have there, and there are bound to be ones on those disks thatyou don't know. You might as well learn them if they are in your range, since you have the disks?
I never have trouble finding new songs to sing, even though I know thousands....there are many songs I like but haven't had time to sit down and learn. I have MP3's of the songs and I try to listen to them whenever I can. I like to listen to a song over and over again to really know it (especially if it's brand new to me). Then once I know it pretty well, I print out the lyrics and learn it REALLY well, making notations on the lyrics as I go. Then I sing it over and over along with the MP3, then I do the same thing with the karaoke version (if I have it). Then I try recording it. Then, after I find a recording I like, I try it in live karaoke.
There have been a few times when I tried a song in live karaoke that I did not go through this with, but usually they are songs I have known pretty well for many years....but that's just me
I don't like to mess up and I've found that the only way to avoid that is to learn it really well first.
Another way, then, to find new songs is to download a bunch of songs by artists whose stuff you already know and like. I have done that many times....it works pretty well. Like, if you enjoy for instance singing one or two songs by Pat Benatar, learn some more songs by her.
Of course another good way to find new songs is to listen to the songs that people do here on SS....if you like it, learn it!
I agree that Mariah Carey is very difficult to sing. I feel the same way about Whitney Houston and Celine Dion. Not only are they very high, but they have all those trills, runs, etc. Those are hard to learn if they don't come to you "naturally", which they don't to me...and they are very high, usually, and then of course to make them SOUND natural is also hard work. Their singing is a lot harder than your average pop singer's singing.
Good luck!